Generalized parity–time symmetry condition for enhanced sensor telemetry

Wireless sensors based on micromachined tunable resonators are important in a variety of applications, ranging from medical diagnosis to industrial and environmental monitoring. The sensitivity of these devices is, however, often limited by their low quality (Q) factor. Here, we introduce the concept of isospectral party–time–reciprocal scaling (PTX) symmetry and show that it can be used to build a new family of radiofrequency wireless microsensors exhibiting ultrasensitive responses and ultrahigh resolution, which are well beyond the limitations of conventional passive sensors. We show theoretically, and demonstrate experimentally using microelectromechanical-based wireless pressure sensors, that PTX-symmetric electronic systems share the same eigenfrequencies as their parity–time (PT)-symmetric counterparts, but crucially have different circuit profiles and eigenmodes. This simplifies the electronic circuit design and enables further enhancements to the extrinsic Q-factor of the sensors. Wireless sensors employing a generalized parity–time-symmetry telemetric sensing technique exhibit finer spectral resolution and more sensitive frequency response compared to conventional passive sensors.